Archery stabilizers mount to the back of a bow riser by screwing into a standardized threaded hole that come standard on almost all bows sold today. The stabilizer adds weight out in front of the archer to help steady the bow during the draw cycle of the arrow and hold steady while at full draw. This results in better aiming of the arrow.
Once the arrow is in flight, a tremendous amount of energy is released, causing the bow to torque and twist in the archer's hand. The stabilizer helps resist this torque similar to the way a tightrope walker will use a long pole with weighted ends. The longer the pole and the heavier the end weights, the more control the tightrope walker will have over torque. The same is true of archery stabilizers.
Another benefit can be to reduce felt vibration during the shot. When the arrow is released the force will travel through the bow limbs, riser and into the archers hand. A stabilizer will allow the vibration forces to travel away from the archer's hand, and down the length of the stabilizer.
All Stabilizers on the market operate with a similar principle; keep the added weights as far from the archer as possible, therefore creating the most stability at a given length. More mass weight at the distal end of the stabilizer typically means a steadier shot. The problem this creates is that by adding more weight further away from the bow attachment, the more rigid the stabilizer tube must become. The stiffer the rod the higher the rod vibration, also called resonance vibration. What this means to the archer is that the energy that was transmitted through the bow and away from the archer through the stabilizer ends up coming back to the archers hand through the same path through the stabilizer. What is required is an archery stabilizer which is less prone to resonance vibration.
The problem of resonance vibration is currently tackled by two methods. The first method is to add a rubber material around the outside of the stabilizer tube (like a donut) or inside the tube (like a plug) to absorb some vibration in a contact area where the rubber and tube intersect. The second way is to change the profile of the stabilizer rod to have a non-constant cross section, through a tapered profile or variable wall thickness.